Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Warning 9.5.4.14. The inclusion functors $\operatorname{\mathcal{QC}}^{\operatorname{LPr}} \hookrightarrow \operatorname{\mathcal{QC}}_{\leq \Omega } \hookleftarrow \operatorname{\mathcal{QC}}^{\operatorname{RPr}}$ do not preserve small colimits. For example, the initial object of $\operatorname{\mathcal{QC}}_{\leq \Omega }$ is the empty $\infty $-category, which is not presentable.